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Fitting classes of CC-groups

Published online by Cambridge University Press:  13 July 2011

Martyn R. Dixon
Martyn R. Dixon
Affiliation:
Department of MathematicsUniversity of AlabamaP.O. Box 1416Tuscaloosa, AL 35487, USA
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The theory of Fitting classes is, by now, a well established part of the theory of finite soluble groups. In contrast, Fitting classes have received rather scant attention in infinite groups, although some recent work of Beidleman and Karbe [2] and Beidleman, Karbe and Tomkinson [3] suggest that one can obtain results in this direction. The paper [2], cited above, in fact generalizes earlier work of Tomkinson [9] to the class of locally soluble FC-groups. The present paper is concerned with the theory of Fitting classes in a class of groups somewhat similar to the class of FC-groups, namely the class of CC-groups, introduced by Polovickiǐ in [6]. A group G is a CC-group if G/CG(xG) is a Černikov group for all x ∈ G where, as in the rest of this paper, we use the standard group theoretic notation of [7]. Recently, Alcázar and Otal [1] have shown how to generalize results of B. H. Neumann [5] to the class of CC-groups. The main purpose of the present note is to illustrate further how one can handle CC-groups, in an analogous manner to FC-groups, by using techniques similar to those used in [1] and [4].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 475 - 479
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

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